Optimal. Leaf size=24 \[ 1+\frac {e^2+\frac {1}{2} (-5-x)}{x}+3 x+\log (5) \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps
used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 14}
\begin {gather*} 3 x-\frac {5-2 e^2}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {5-2 e^2+6 x^2}{x^2} \, dx\\ &=\frac {1}{2} \int \left (6+\frac {5-2 e^2}{x^2}\right ) \, dx\\ &=-\frac {5-2 e^2}{2 x}+3 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 0.75 \begin {gather*} -\frac {5-2 e^2}{2 x}+3 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 16, normalized size = 0.67
method | result | size |
norman | \(\frac {3 x^{2}+{\mathrm e}^{2}-\frac {5}{2}}{x}\) | \(14\) |
default | \(3 x -\frac {-2 \,{\mathrm e}^{2}+5}{2 x}\) | \(16\) |
risch | \(3 x +\frac {{\mathrm e}^{2}}{x}-\frac {5}{2 x}\) | \(16\) |
gosper | \(\frac {6 x^{2}+2 \,{\mathrm e}^{2}-5}{2 x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 15, normalized size = 0.62 \begin {gather*} 3 \, x + \frac {2 \, e^{2} - 5}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 16, normalized size = 0.67 \begin {gather*} \frac {6 \, x^{2} + 2 \, e^{2} - 5}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.50 \begin {gather*} 3 x + \frac {-5 + 2 e^{2}}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.62 \begin {gather*} 3 \, x + \frac {2 \, e^{2} - 5}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.03, size = 12, normalized size = 0.50 \begin {gather*} 3\,x+\frac {{\mathrm {e}}^2-\frac {5}{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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